Final answer:
The derivative of y = 4x^3 with respect to x is 12x^2. The reference to the function fx(x) = 7e^(-7x) is not directly related to the derivative of y and therefore is not part of the solution for this question.
Step-by-step explanation:
The derivative of y = 4x^3 with respect to x is found by using the power rule of differentiation. Apply this rule by multiplying the exponent by the coefficient and then subtract one from the exponent to obtain the new power of x. Therefore, the derivative dy/dx is 12x^2.
As for the function fx(x) = 7e^(-7x), it appears to be unrelated to the original question regarding the derivative of y with respect to x. However, the presence of this function suggests that the student might be looking for a connection between these functions, which could be clarified by further instruction or examples.
The given range 0 < x < infinity indicates that we are considering the behavior of the derivative of y over all positive values of x.